The $p-$sphere and the geometric substratum of power law probability distributions

Details The $p-$sphere and the geometric substratum of power law probability distributions The $p-$sphere and the geometric substratum of power law probability distributions

2005-05-06

arxiv.org/abs/cond-mat/0505161v1

Physics

Condensed Matter

Statistical Mechanics

10 pages

Scientific paper

10.1016/j.physleta.2005.05.027

Links between power law probability distributions and marginal distributions of uniform laws on $p$-spheres in $\mathbb{R}^{n}$ show that a mathematical derivation of the Boltzmann-Gibbs distribution necessarily passes through power law ones. Results are also given that link parameters $p$ and $n$ to the value of the non-extensivity parameter $q$ that characterizes these power laws in the context of non-extensive statistics.

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